Cours de simulation distribueel

1SuP GaliléeL’école d’ingénieurs de l’Institut GaliléeSpécialité MACS 3ème annéeSIMULATION DISTRIBUEEL. Halpern et J. Ryanc INSTITUTGALILEE,99avenueJean-Baptiste-Clément93430 VILLETANEUSE2008/20092Ingénieurs P.U.F. MasterMathématiques appliquées Ho Chi Minh Universityet Calcul Scientifique of Natural SciencesThis course has been given in the years 2007-2009asa graduate course attheUniversity Paris13,intheengineering schoolofappliedmathematicsandscientific computation Sup Galilée, and at the Ho Chi Minh City Universityof Natural Sciences, hosted by the PUF in the department of mathematics.The authors are very grateful to Pr. Zinsmeister for the programm, andto Pr. Duc for his thorough training of the students, and warm welcome inHCMCity.Table des matières1 Foreword 72 Multigrid methods 92.1 Modal analysis in a simple case . . . . . . . . . . . . . . . . . 92.1.1 Simple methods . . . . . . . . . . . . . . . . . . . . . . 102.1.2 Convergence rate . . . . . . . . . . . . . . . . . . . . . 112.1.3 The V- cycle process . . . . . . . . . . . . . . . . . . . 15∞2.1.4 L estimates . . . . . . . . . . . . . . . . . . . . . . . 212.1.5 Number of elementary operations . . . . . . . . . . . . 222.2 The finite elements multigrid algorithm . . . . . . . . . . . . . 222.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . 222.2.2 Discrete norm . . . . . . . . . . . . . . . . . . . . . . . 252.2.3 Definition of the multigrid algorithm . . . . . . . . ...